Eğri uzay-zamanda dirac-tipi işlemcilerin simetrileri ve Killing-yano formları
Özet
Clifford calculus and spinor calculus on manifolds are studied. As generalizations of Killing and conformal Killing vector fields, Killing-Yano (KY) and conformal Killing-Yano (CKY) forms are considered. Calculations for explicit forms of KY forms on spherically symmetric space-times are done. First-order symmetries of Dirac equation with and without interaction terms on a curved background are established. It has been seen that in the existence of a interaction term, the symmetries of the Dirac equation are written from KY forms which Clifford commute with the force field. As a generalization of the Dirac equation to the differential forms, Kähler equation and its first-order symmetries are studied. Relations between conservation laws and KY forms are also considered. Basic gravitational conserved currents constructed from KY forms are established. Some basic geometric relations for some special cases are found